Emergence of Flavor Mixing, CKM Hierarchy, and CP Violation from a Resonant Brane Model (ERB) – Preprint & Stability Proof

Emergence of Flavor Mixing, CP Violation, and Mass Hierarchy from a Resonant Brane Model — ERB Model Version 13 We present Version 13 of the Emergent Resonant Brane (ERB) model. The central advance is the identification of the relativistic origin of the two fundamental ERB parameters. δ = 1/2 as brane mass ratio. The lattice tension of the two primary branes satisfies ε_B/ε_A = m_B/m_A at fixed oscillation frequency. Since ε_B/ε_A = 3/2, the primary branes have mass ratio m_B/m_A = 3/2, and δ = (m_B − m_A)/m_A = 1/2 exactly. The Isospin Master Equation is not a quantum postulate imposed from outside — it is a material property of the vacuum medium. The asymmetry was always there, at the source. γ = 2π as common denominator. Two branes with mass ratio 3/2 can only interfere stably when their phases close on a common period. The ground state (Q = 1, single vortex) corresponds to one full 2π rotation — the smallest common phase of two oscillators with ratio 3/2. γ = 2π is necessary, not empirical. α = γ − 1 as time-dilation exponent. Each generation rotates with orbital velocity v_i = ω·r_i. In the ultrarelativistic limit the Lorentz factor γ_i ~ r_i, and the rest mass scales as m₀_i ~ r_i^(α−1), giving m_i ~ r_i^α — exactly the ERB log-ladder formula. The candidate α = 2π − 1 ≈ 5.28 (2.9% from measured 5.13) means one full Flavor Clock rotation accumulates exactly this time dilation. Analytical proof is the next open question. All previous results are retained: MAE(CKM) = 2.32×10⁻⁵, J = −3.08×10⁻⁵ (PDG: 3.0×10⁻⁵), δ = 1/2 exact (0.000% cost), Ω_up/Ω_dn = 5/3 (zero free parameters), M_scale = Λ_QCD·√(2π) topologically confirmed, GL dynamics proven as overdamped limit of V_ERB (v12). The complete derivation chain from v4 to v13 is provided in the companion notebook ERB_Complete_v13.ipynb. The Standard Model flavour sector reduces to one number: m_B/m_A = 3/2. Everything else is emergent.